Preprint

Kernels of categorical resolutions of nodal singularities, arXiv:2209.12853, joint with Warren Cattani, Franco Giovenzana, Pablo Magni, Luigi Martinelli, Laura Pertusi, Jieao Song, submitted

In this paper we study derived categories of nodal singularities. We show that for all nodal singularities there is a categorical resolution whose kernel is generated by a 2 or 3-spherical object, depending on the dimension. We apply this result to the case of nodal cubic fourfolds, where we describe the kernel generator of the categorical resolution as an object in the bounded derived category of the associated degree six K3 surface. This paper originated from one of the problem sessions at the Interactive Workshop and Hausdorff School "Hyperkähler Geometry", Bonn, September 6-10, 2021.

Stability condition on Calabi-Yau threefold of complete intersection of quadratic and quartic hypersurfaces, arXiv:2108.08934, Forum of Mathematics, Sigma, accepted

In this paper, we proved the existence of the stability on X_2,4 inside P⁵ by prove the Bogomolov-Gieseker stability holds on X_2,4. The method in this paper extended the method by Dr. Chunyi Li for quintic threefolds by allowing the intermediate surface to be a K3 surface.